This article is cited in 3 papers

Independent axiomatizability of quasivarieties of torsion-free nilpotent groups

A. I. Budkin

Altai State University, Barnaul

Abstract: Let $N$ be a quasivariety of torsion-free nilpotent groups of class at most two. It is proved that the set of subquasivarieties in $N$, which have no independent basis of quasi-identities and are generated by a finitely generated group, is infinite. It is stated that there exists an infinite set of quasivarieties $M$ in $N$ which are generated by a finitely generated group and are such that for every quasivariety $K$ ($M\varsubsetneq K\subseteq N$), an interval $[M,K]$ has the power of the continuum in the quasivariety lattice.

Keywords: nilpotent group, quasivariety, variety, independent basis of quasi-identities.

UDC: 512.54

Received: 01.01.2021
Revised: 24.08.2021

DOI: 10.33048/alglog.2021.60.201

 English version: Algebra and Logic, 2021, 60:2, 79–88

Bibliographic databases:

• 
•